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## Managing Quality

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**Managing Quality**6 PowerPoint presentation to accompany Heizer and Render Operations Management, 10e Principles of Operations Management, 8e PowerPoint slides by Jeff Heyl**Outline**• Defining Quality • Implications of Quality • Ethics and Quality Management • Total Quality Management • Continuous Improvement • Six Sigma • Employee Empowerment • TQM in Services • Statistical Process Control (SPC) • Control Charts for Variables • Control Charts for Attributes • Process Capability • Process Capability Ratio (Cp) • Process Capability Index (Cpk)**Learning Objectives**Define quality and TQM Explain Six Sigma Explain the use of a control chart Build -charts and R-charts Build p-charts Explain process capability and compute Cp and Cpk**Sales Gains via**• Improved response • Flexible pricing • Improved reputation Improved Quality Increased Profits Reduced Costs via • Increased productivity • Lower rework and scrap costs • Lower warranty costs Two Ways Quality Improves Profitability Figure 6.1**Defining Quality**The totality of features and characteristics of a product or service that bears on its ability to satisfy stated or implied needs American Society for Quality • Different Views • User-based • Manufacturing-based • Product-based**Performance**Features Reliability Conformance Durability Serviceability Aesthetics Perceived quality Value Key Dimensions of Quality**Ethics and Quality Management**• Operations managers must deliver healthy, safe, quality products and services • Poor quality risks injuries, lawsuits, recalls, and regulation • Organizations are judged by how they respond to problems • All stakeholders much be considered**Create consistency of purpose**• Lead to promote change • Build quality into the product; stop depending on inspections • Build long-term relationships based on performance instead of awarding business on price • Continuously improve product, quality, and service • Start training • Emphasize leadership Deming’s Fourteen Points Table 6.2**Drive out fear**• Break down barriers between departments • Stop haranguing workers • Support, help, and improve • Remove barriers to pride in work • Institute education and self-improvement • Put everyone to work on the transformation Deming’s Fourteen Points Table 6.2**Continuous Improvement**• Represents continual improvement of all processes • Involves all operations and work centers including suppliers and customers • People, Equipment, Materials, Procedures**Lower limits**Upper limits 2,700 defects/million 3.4 defects/million 6 Mean ±3 ±6 Six Sigma Program • A highly structured program developed by Motorola • A discipline – DMAIC • Also, • Statistical definition of a process that is 99.9997% capable, 3.4 defects per million opportunities (DPMO) Figure 6.4**Define critical outputs and identify gaps for improvement**Measure the work and collect process data Analyze the data Improve the process Control the new process to make sure new performance is maintained Six Sigma DMAIC Approach**Employee Empowerment**• Getting employees involved in product and process improvements • 85% of quality problems are due to process and material • Techniques • Build communication networks that include employees • Develop open, supportive supervisors • Move responsibility to employees • Build a high-morale organization • Create formal team structures**TQM In Services**• Service quality is more difficult to measure than the quality of goods • Service quality perceptions depend on • Intangible differences between products • Intangible expectations customers have of those products**Statistical Process Control (SPC)**• Variability is inherent in every process • Natural or common causes • Special or assignable causes • Provides a statistical signal when assignable causes are present • Detect and eliminate assignable causes of variation**Natural Variations**• Also called common causes • Affect virtually all production processes • Expected amount of variation • Output measures follow a probability distribution • For any distribution there is a measure of central tendency and dispersion • If the distribution of outputs falls within acceptable limits, the process is said to be “in control”**Assignable Variations**• Also called special causes of variation • Generally this is some change in the process • Variations that can be traced to a specific reason • The objective is to discover when assignable causes are present • Eliminate the bad causes • Incorporate the good causes**Types of Data**Variables Attributes • Characteristics that can take any real value • May be in whole or in fractional numbers • Continuous random variables • Defect-related characteristics • Classify products as either good or bad or count defects • Categorical or discrete random variables**For variables that have continuous dimensions**• Weight, speed, length, strength, etc. • x-charts are to control the central tendency of the process • R-charts are to control the dispersion of the process • These two charts must be used together Control Charts for Variables**For x-Charts when we know s**Upper control limit (UCL) = x + zsx Lower control limit (LCL) = x - zsx where x = mean of the sample means or a target value set for the process z = number of normal standard deviations sx = standard deviation of the sample means = s/ n s = population standard deviation n = sample size Setting Chart Limits**Hour 1**Sample Weight of Number Oat Flakes 1 17 2 13 3 16 4 18 5 17 6 16 7 15 8 17 9 16 Mean 16.1 s = 1 Hour Mean Hour Mean 1 16.1 7 15.2 2 16.8 8 16.4 3 15.5 9 16.3 4 16.5 10 14.8 5 16.5 11 14.2 6 16.4 12 17.3 n = 9 UCLx = x + zsx = 16 + 3(1/3) = 17 ozs LCLx = x - zsx = 16 - 3(1/3) = 15 ozs Setting Control Limits For 99.73% control limits, z = 3**Variation due to assignable causes**Out of control 17 = UCL Variation due to natural causes 16 = Mean 15 = LCL Variation due to assignable causes | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 Out of control Sample number Setting Control Limits Control Chart for sample of 9 boxes**For x-Charts when we don’t know s**Upper control limit (UCL) = x + A2R Lower control limit (LCL) = x - A2R where R = average range of the samples A2 = control chart factor found in Table S6.1 x = mean of the sample means Setting Chart Limits**Sample Size Mean Factor Upper Range Lower Range**n A2 D4 D3 2 1.880 3.268 0 3 1.023 2.574 0 4 .729 2.282 0 5 .577 2.115 0 6 .483 2.004 0 7 .419 1.924 0.076 8 .373 1.864 0.136 9 .337 1.816 0.184 10 .308 1.777 0.223 12 .266 1.716 0.284 Control Chart Factors Table S6.1**Process average x = 12 ounces**Average range R = .25 Sample size n = 5 Setting Control Limits**Process average x = 12 ounces**Average range R = .25 Sample size n = 5 UCLx = x + A2R = 12 + (.577)(.25) = 12 + .144 = 12.144 ounces From Table S6.1 Setting Control Limits**Process average x = 12 ounces**Average range R = .25 Sample size n = 5 UCLx = x + A2R = 12 + (.577)(.25) = 12 + .144 = 12.144 ounces UCL = 12.144 Mean = 12 LCLx = x - A2R = 12 - .144 = 11.857 ounces LCL = 11.857 Setting Control Limits**UCL = 11.524**x – 10.959 LCL – 10.394 11.5 – 11.0 – 10.5 – x Bar Chart Sample Mean | | | | | | | | | 1 3 5 7 9 11 13 15 17 0.8 – 0.4 – 0.0 – Range Chart UCL = 0.6943 R = 0.2125 LCL = 0 Sample Range | | | | | | | | | 1 3 5 7 9 11 13 15 17 Restaurant Control Limits For salmon filets at Darden Restaurants**R – Chart**• Type of variables control chart • Shows sample ranges over time • Difference between smallest and largest values in sample • Monitors process variability • Independent from process mean**Upper control limit (UCLR) = D4R**Lower control limit (LCLR) = D3R where R = average range of the samples D3 and D4 = control chart factors from Table S6.1 Setting Chart Limits For R-Charts**Average range R = 5.3 pounds**Sample size n = 5 From Table S6.1 D4 = 2.115, D3 = 0 UCLR = D4R = (2.115)(5.3) = 11.2 pounds UCL = 11.2 Mean = 5.3 LCLR = D3R = (0)(5.3) = 0 pounds LCL = 0 Setting Control Limits**(a)**These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) UCL (x-chart detects shift in central tendency) x-chart LCL UCL (R-chart does not detect change in mean) R-chart LCL Mean and Range Charts Figure S6.5**(b)**These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) UCL (x-chart does not detect the increase in dispersion) x-chart LCL UCL (R-chart detects increase in dispersion) R-chart LCL Mean and Range Charts Figure S6.5**Control Charts for Attributes**• For variables that are categorical • Good/bad, yes/no, acceptable/unacceptable • Measurement is typically counting defectives • Charts may measure • Percent defective (p-chart) • Number of defects (c-chart)**p(1 - p)**n sp = UCLp = p + zsp ^ ^ LCLp = p - zsp ^ where p = mean fraction defective in the sample z = number of standard deviations sp = standard deviation of the sampling distribution n = sample size ^ Control Limits for p-Charts Population will be a binomial distribution, but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics**Sample Number Fraction Sample Number Fraction**Number of Errors Defective Number of Errors Defective 1 6 .06 11 6 .06 2 5 .05 12 1 .01 3 0 .00 13 8 .08 4 1 .01 14 7 .07 5 4 .04 15 5 .05 6 2 .02 16 4 .04 7 5 .05 17 11 .11 8 3 .03 18 3 .03 9 3 .03 19 0 .00 10 2 .02 20 4 .04 Total = 80 (.04)(1 - .04) 100 80 (100)(20) sp = = .02 p = = .04 ^ p-Chart for Data Entry**.11 –**.10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – UCLp = 0.10 UCLp = p + zsp = .04 + 3(.02) = .10 ^ Fraction defective p = 0.04 LCLp = p - zsp = .04 - 3(.02) = 0 ^ LCLp = 0.00 | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number p-Chart for Data Entry**.11 –**.10 – .09 – .08 – .07 – .06 – .05 – .04 – .03 – .02 – .01 – .00 – UCLp = 0.10 UCLp = p + zsp = .04 + 3(.02) = .10 ^ Fraction defective p = 0.04 LCLp = p - zsp = .04 - 3(.02) = 0 ^ LCLp = 0.00 | | | | | | | | | | 2 4 6 8 10 12 14 16 18 20 Sample number p-Chart for Data Entry Possible assignable causes present**Variables Data**Using an x-Chart and R-Chart • Observations are variables • Collect 20 - 25 samples of n = 4, or n = 5, or more, each from a stable process and compute the mean for the x-chart and range for the R-chart • Track samples of n observations each. Which Control Chart to Use Table S6.3**Attribute Data**Using the p-Chart • Observations are attributes that can be categorized as good or bad (or pass–fail, or functional–broken), that is, in two states. • We deal with fraction, proportion, or percent defectives. • There are several samples, with many observations in each. For example, 20 samples of n = 100 observations in each. Which Control Chart to Use Table S6.3**UCL**UCL UCL UCL UCL UCL Target Target Target Target Target Target LCL LCL LCL LCL LCL LCL Patterns in Control Charts Erratic behavior. Trends in either direction, 5 plots. Progressive change. Two plots very near lower (or upper) control. Run of 5 above (or below) central line. One plot out above (or below). Process is “out of control.” Normal behavior. Process is “in control.”**Process Capability**• The natural variation of a process should be small enough to produce products that meet the standards required • A process in statistical control does not necessarily meet the design specifications • Process capability is a measure of the relationship between the natural variation of the process and the design specifications**Upper Specification - Lower Specification**6s Cp = Process Capability Ratio • A capable process must have a Cp of at least 1.0 • Does not look at how well the process is centered in the specification range • Often a target value of Cp = 1.33 is used to allow for off-center processes • Six Sigma quality requires a Cp = 2.0**Process mean x = 210.0 minutes**Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification 6s Cp = Process Capability Ratio Insurance claims process**Process mean x = 210.0 minutes**Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification 6s Cp = 213 - 207 6(.516) = = 1.938 Process Capability Ratio Insurance claims process**Process mean x = 210.0 minutes**Process standard deviation s = .516 minutes Design specification = 210 ± 3 minutes Upper Specification - Lower Specification 6s Cp = 213 - 207 6(.516) = = 1.938 Process Capability Ratio Insurance claims process Process is capable**UpperSpecification - xLimit**3s Lowerx - Specification Limit 3s Cpk = minimum of , Process Capability Index • A capable process must have a Cpk of at least 1.0 • A capable process is not necessarily in the center of the specification, but it falls within the specification limit at both extremes**New process mean x = .250 inches**Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches Process Capability Index New Cutting Machine**New process mean x = .250 inches**Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches (.251) - .250 (3).0005 Cpk = minimum of , Process Capability Index New Cutting Machine**New process mean x = .250 inches**Process standard deviation s = .0005 inches Upper Specification Limit = .251 inches Lower Specification Limit = .249 inches (.251) - .250 (3).0005 .250 - (.249) (3).0005 Cpk = minimum of , .001 .0015 Cpk = = 0.67 Process Capability Index New Cutting Machine Both calculations result in New machine is NOT capable

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